Nov 9, 2003 - Jiawen Yang is associate professor of international business and international ... How good is the Big Mac index as a guide for currency valuation? .... estimated exchange rate is smaller than the exchange rate determined in ...
The Big Mac Index and the Valuation of the Chinese Currency Jiawen Yang* School of Business and Public Management The George Washington University
November 2003
*
Jiawen Yang is associate professor of international business and international affairs at the School of Business and Public Management, The George Washington University. I gratefully acknowledge the research support from the Center for the Study of Globalization (CSG) of the George Washington University for the Chinese currency research project. I thank John Forrer, Min Chan Pyo, Haiyan Yin, and seminar participants at the George Washington University for comments. Research assistance from Hui He and Vivian Liu is highly appreciated.
The Big Mac Index and the Valuation of the Chinese Currency Abstract The Big Mac index has been used as one of the justifications for the claim that the Chinese currency, the Renminbi (RMB), is undervalued at the current exchange rate of 8.28 yuan to the dollar. This note intends to evaluate the Big Mac index as a guide for currency valuation and analyze the value of the RMB. Since the Big Mac index fails to account for the non-tradable component in its pricing, it is a misleading measure for currency valuation for countries whose income levels are lower than the benchmark currency countries. The RMB is being overvalued by the index since China’s per capita income is significantly lower than that of the United States.
The Big Mac Index and the Valuation of the Chinese Currency Jiawen Yang In 1986 the Economist magazine began publishing a survey of prices of Big Macs in a number of countries as “a rough-and ready guide to whether a currency is under- or over-valued,” in the hope of making economic theory more digestible (Economist 1991). The survey started to cover China in 1992 (with 1996 as an exception). The survey has shown consistently that the RMB has been undervalued (See Table 1). In 2003, the Big Mac exchange rate between the RMB and the U.S. dollar was 3.65 yuan/dollar versus the actual exchange rate at 8.28 yuan/dollar, implying that the Chinese currency was undervalued by 56% against the dollar.1 While the Big Mac index is only a “medium-rare guide to whether currencies are trading at the right exchange rates (Economist, 1986),” it has been regarded as “a pretty good indicator,” and has the added benefit of being a measure that “lay people can understand (Bender 2003).” Policy makers and business executives do use the index to support their recent claims that the Chinese currency is undervalued. Table 1 Valuation of RMB Based on Big Mac Prices
Year
Prices RMB (Yuan)
Prices in dollars
Actual exchange rate
1992 1993 1994 1995 1997 1998 1999 2000 2001 2002 2003
6.3 8.5 9.0 9.0 9.7 9.9 9.9 9.9 9.9 10.5 9.9
2.19 1.50 1.03 1.05 1.16 1.20 1.20 1.20 1.20 1.27 1.20
5.44 5.68 8.70 8.54 8.33 8.28 8.28 8.28 8.28 8.28 8.28
PPP RMB under (-) / Implied over(+) valuation exchange % rate 2.88 3.73 3.91 3.88 4.01 3.87 4.07 3.94 3.90 4.22 3.65
-47 -34 -55 -55 -52 -53 -51 -52 -53 -49 -56
Note: Sources: The Economist, various issues There was no data for China for the 1996 survey.
1
One should note that the reference for the Big Mac index – the price of a Big Mac in the United States – varies significantly even within the United States. The 1989 Economist survey found that the price of a Big Mac varied much more in America than within other countries. The price ($2.48) in Manhattan was about 23% higher than the average of four U.S. cities ($2.02), or the average dollar in the four U.S. cities was undervalued by about 18.5% against the dollar in Manhattan.
1
How good is the Big Mac index as a guide for currency valuation? As the price of a Big Mac must cover not only the cost of ground meat and buns, which are supposed to be tradable, but also the cost of non-tradable local services such as labor, rent, and electricity, one has to dichotomize the ingredients in the analysis of the Big Mac index. The price of a Big Mac in the United States can be specified as follows: P$ = P T, $ T US + W$ LUS
Where T: L: P T, $: W$ :
(1)
Ingredients that can be traded across countries. Labor and other local inputs required preparing and serving the Big Mac. Prices of traded ingredients in the United States. Cost of local inputs (mainly wages) in the United States.
Similarly, the price of a Big Mac in China is specified as PRMB = P T, RMB TChina + WRMB LChina
(2)
The Big Mac is presumably a homogeneous product across countries and it is sensible to assume that the tradable ingredients, TUS and TChina, are the same. For simplicity, we normalize them as 1. Labor inputs should represent the main portion of the non-tradable ingredients, LUS and LChina. Labor productivity in preparing and serving the Big Mac should not be much different in the United States and China. This assumption, while intuitively plausible, is also evidenced in Balassa (1964) and Samuelson (1964). In their reappraisal of the purchasing power parity doctrine, Balassa (1964) and Samuelson (1964) highlighted the importance of non-traded goods (services) in the relationship between prices and exchange rates. They assumed that the labor forces of poor countries are less productive than those of rich countries in the tradables sector but that international productivity differences in nontradeables are negligible. Given this assumption, we again normalize the nontradable inputs for the Big Mac in both countries as 1. Thus equations (1) and (2) become P$ = P T, $ + W$
(3)
PRMB = P T, RMB + WRMB
(4)
The exchange rate (expressed as yuan to the dollar) based on Big Mac prices can then be expressed as:
E Big Mac
=
PRMB P$
=
PT , RMB + WRMB
(5)
PT ,$ + W$
The first part of equation (5) is exactly how the Economist magazine formulates its “implied PPP of the dollar.” Following Balassa (1964), we argue that, in the absence of trade restrictions, the market (or actual) exchange rate equates the prices of traded goods, with allowance made for transportation costs. Thus, P T, RMB = ET P T, $
(6)
2
Where ET is the exchange rate (yuan/$) that is determined in the traded goods market. Then Equation (5) becomes
E Big Mac
= ET
PT ,$ + (WRMB ET ) PT ,$ + W$
(7)
Equation (7) yields an important comparison between the Big Mac implied exchange rate and the exchange rate determined by the traded goods market. The conformity between the two exchange rates hinges crucially on (1) the proportion of the cost of traded ingredients in the total dollar cost of the Big Mac, PT,$ / (PT,$ + W$), and (2) the difference between the wages rates (costs of nontradable ingredients) as measured in dollars, (WRMB/ET) as compared with W$. As the proportion of cost of the tradable ingredients approaches 1 (That is, all ingredients are tradable – no local services involved), the two exchange rates will converge. On the other hand, if all the ingredients are nontradable, the conformity of the two exchange rates depends entirely on the convergence of the wage rates (or costs of the nontradable ingredients) in the two countries. When the wage rates are equal, so are the two exchange rates. But as long as (WRMB/ET) < W$, we have PT ,$ + (WRMB E ) PT ,$ + W$
< 1
And
E Big Mac
(8)
(9)
< ET
That is, as long as the wage rates in China are lower than that in the United States, the Big Mac estimated exchange rate is smaller than the exchange rate determined in the goods market. It is known to all that China, despite its rapid economic growth in the past two decades, its per capita income is still among the lowest in the world. According to the World Bank, per capita income in the United States in 2002 was $35,060 while that for China was $940. That is, the U.S. per capita income was 37.3 times as much as that of China. Even based on the World Bank’s estimate of China’s PPP adjusted per capita income - $4,390 in 2002, the U.S. per capita income is still about 8 times as high as that for China. Table 2 presents the quarterly and hourly wage rates for workers employed in different types of enterprises in China. The average hourly wage in the first quarter of 2003 was only $.77 for Chinese workers. One should note that the rural workers (farmers) – the majority of China’s population - cannot even earn that rate on average. For comparison, the average hourly wages were $15.46 in October 2003, about 20 times that for Chinese workers.2
2
The average hourly wages for the private sector in the United States is obtained from the U.S. Department of Labor, The Employment Situation: October 2003, available at http://www.bls.gov/news.release/empsit.nr0.htm (accessed November 9, 2003).
3
According to McDonald’s 2002 financial report, tradable ingredients (food and paper) were about 25% of total sales.3 That is, out of the average price of $2.71 for a Big Mac in the United States in 2003, about $0.69 represented tradable ingredients and $2.02 for non-tradable ingredients. Assume that the tradable ingredients in China cost the same but the non-tradable ingredients were a quarter of the U.S. costs, not an unreasonable assumption as discussed above, then the Big Mac should have sold for $1.19! This estimate is strikingly close to the Economist survey price - $1.20 in China. Table 2 Workers’ Compensation in China: First Quarter 2003
Type of Enterprises
Number of People Employed
Average Compensation Quarterly
Hourly
000
%
in Yuan
In USD
In USD
108,343
100.00%
3,139.00
379.11
0.73
State-owned Enterprises
70,702
65.26%
3,243.00
391.67
0.75
Township Enterprises
10,884
10.05%
1,883.00
227.42
0.44
Other
26,757
24.70%
3,379.00
408.09
0.78
Total
Notes: Other enterprises include joint ventures with foreign enterprises and large privately owned enterprises. Hourly compensation is based on 40 hour/week and 13 weeks in the quarter. The prevailing exchange rate of 8.28 yuan/USD is used for conversion. Source: National Bureau of Statistics of China, Compensation for Employees in Urban Areas, http://www.stats.gov.cn/tjsj/jdsj/1200305070150.htm. Accessed June 11, 2003.
The conclusion that low per capita income countries’ currencies tend to be undervalued based on purchasing power parity (PPP) has been well documented in the academic literature. Balassa (1964) points out that, since services (non-tradable) enter the calculation of purchasing power parities but do not directly affect exchange rate, the purchasing power parity based exchange rate, measured as currency units for the low wage country per unit of the currency for high wage country, will be lower than the equilibrium rate of exchange. Balassa points out further that the greater are productivity differentials in the production of traded goods between two countries, the larger will be the differences in wages and in the prices of services and, correspondingly, the greater will be the gap between purchasing power parity and the equilibrium exchange rate. Instead of relying on the differential productivity postulate, Bhagwati (1984) and Kravis and Lipsey (1983) resort to differences in endowments of capital and labor to explain the lower price levels of poor countries and the undervaluation of currencies for these countries.
3
McDonald’s 2002 Financial Report, available at http://www.mcdonalds.com/corporate/investor/financialinfo/investorpub/financial/page16/ada1/index.html. Accessed November 21, 2003.
4
Table 3 Big Mac Valuation and Per Capita Income - 2002 2002
United States Argentina South Africa Russia China Philippines Thailand Malaysia Hong Kong Poland Brazil Australia Czech Rep Hungary Indonesia New Zealand Singapore Japan Canada Chile Mexico S. Korea Peru Sweden Britain Venezuela Denmark Turkey Switzerland Sources:
Local currency units
Prices in local currency
Prices in dollars
Actual Implied PPP Local currency exchange of the dollar under (-) rate 4/23/02 /over(+) valuation, %
GNP per Capita $ (2002)
PPP GNP per GNP per PPP GNP Capita $ capita as per capita as (2002) compared compared with US with US
$ 2.49 2.49 35,060 35,060 1.00 1.00 Peso 2.50 0.78 3.13 1.00 -68 4,060 9,930 0.12 0.28 Rand 9.70 0.87 3.90 10.90 -64 2,600 9,870 0.07 0.28 Ruble 39.00 1.25 31.20 15.70 -50 2,140 7,820 0.06 0.22 Yuan 10.50 1.27 8.28 4.22 -49 940 4,390 0.03 0.13 Peso 65.00 1.28 26.10 51.00 -49 1,020 4,280 0.03 0.12 Baht 55.00 1.27 43.30 22.10 -49 1,980 6,680 0.06 0.19 M$ 5.04 1.33 2.02 3.80 -47 3,540 8,280 0.10 0.24 HK$ 11.20 1.40 4.50 7.80 -42 24,750 26,810 0.71 0.76 Zloty 5.90 1.46 2.37 4.04 -41 4,570 10,130 0.13 0.29 Real 3.60 1.55 1.45 2.34 -38 2,850 7,250 0.08 0.21 A$ 3.00 1.62 1.20 1.86 -35 19,740 26,960 0.56 0.77 Koruna 56.28 1.66 22.60 34.00 -33 5,560 14,500 0.16 0.41 Forint 459 1.69 184.00 272.00 -32 5,280 12,810 0.15 0.37 Rupiah 16,000 1.71 6426 9430 -32 710 2,990 0.02 0.09 NZ$ 3.95 1.77 1.59 2.24 -29 13,710 20,020 0.39 0.57 S$ 3.30 1.81 1.33 1.82 -27 20,690 23,090 0.59 0.66 Yen 262.00 2.01 130.00 105.00 -19 33,550 26,070 0.96 0.74 C$ 3.33 2.12 1.34 1.57 -15 22,300 28,070 0.64 0.80 Peso 1,400 2.16 562.00 655.00 -14 4,260 9,180 0.12 0.26 Peso 21.90 2.37 8.80 9.28 -5 5,910 8,540 0.17 0.24 Won 3,100 2.36 1304 1245 -5 9,930 16,480 0.28 0.47 New Sol 8.50 2.48 3.41 3.43 -1 2,050 4,800 0.06 0.14 SKr 26.00 2.52 10.40 10.30 1 24,820 25,080 0.71 0.72 Pound 1.99 2.88 1.25 1.45 16 25,250 25,870 0.72 0.74 Bolivar 2,500 2.92 1004 857 17 4,090 5,080 0.12 0.14 DKr 24.75 2.96 9.94 8.38 19 30,290 29,450 0.86 0.84 Lira 4,000,000 3.06 1606426 1324500 21 2,500 6,120 0.07 0.17 SFr 6.30 3.81 2.53 1.66 53 37,930 31,250 1.08 0.89 Big Mac prices and valuation from The Economist (2002); Per capita GNP data from World Bank, World Development Report, 2003.
5
The relationship between wages/price levels and currency valuation is evident in the Big Mac prices and currency valuations based on these prices. Table 3 presents the Big Mac valuation data from the Economist survey for 2002 and data for per capita income. The correlation between the Big Mac valuation against the U.S. dollar and the normalized income level using the U.S. per capita income as the benchmark is positive (0.5248) and statistically significant.4 This relationship is plotted in Figure 1. Figure 1 Correlation between Per Capita Income and Big Mac Valuation Big Mac Valuation and Per Capital Income Big Mac Valuation
60 40 20 0 -20 -40 -60 -80 0.00%
20.00%
40.00%
60.00%
80.00%
100.00% 120.00%
Per Capital income as share of US
Based on our analysis of the Big Mac standard, we conclude that, given that labor cost is lower in China than in the United States, PPP implied value of the dollar as measured in the Chinese currency should be less than the exchange rate determined by the traded goods market. In other words, the PPP implied value of the RMB should be higher than the value of the RMB determined in the traded goods market. To generalize, the exchange rates for currencies of low-income countries tend to be undervalued based on PPP standards. Or PPP standards tend to overestimate the value of currencies of low-income countries. Given that China’s labor cost and rental are significantly lower than that of the United States, the relatively lower price of Big Mac in China and hence the derived under-valuation should not be a surprise. The under-valuation of the RMB or the overvaluation of the U.S. dollar, as judged by the Big Mac standard, is a natural result of the non-tradable nature of the product and the wages differences in the two countries. Samuelson (1964) pointed out about four decades ago that professors, “particularly cultured ones, are particularly prone to infer an overvaluation of the dollar by the cheapness abroad of personal services (maids, tenors, and Doctors of Philosophy).” By this reasoning, every prosperous region has a chronically overvalued currency. He illustrated the nontradable nature of services by saying that, patently, he could not import cheap Italian haircuts, nor could Niagara-Falls honeymoons be exported. By the same token, American workers would not go to China in 2003 to buy Big Mac hamburgers for lunch, even though the Big Mac hamburger costs less than that of the United States in 2003. 4
Based on the PPP GNP per capita, this correlation is 0.4031, still positive and statistically significant. This smaller correlation is expected when the income levels are adjusted with PPP.
6
Thus, currency valuations based on such measures should not be taken as the basis for exchange rate policy recommendations. However, the RMB should revalue if the gap in productivity and labor compensation between the two countries narrows over time.
7
References Balassa, Bela. 1964. “The Purchasing Power Parity Doctrine: A Reappraisal.” Journal of Political Economy, Vol. 72, No 6 (December): 584-596. Bhagwati, Jagdish N. 1984. “Why Are Services Cheaper in the Poor Countries?” Economic Journal 94 (June): 279-280. Bender, Jay. 2003. Testimony of Jay Bender, President, Falcon Plastics, Inc, On Behalf of the National Association of Manufacturers Before the Committee on Small Business of the House of Representatives On the Impact of Chinese Currency Manipulation on Small Manufacturers and Exporters. June 25. http://www.nam.org/. Accessed September 28, 2003. The Economist, various issues from 1986 to 2003. Kravis, Irving B. and Robert E. Lipsey. 1983. Toward an Explanation of National Price Levels. Princeton Studies in International Finance 52, Princeton University. November. Samuelson, Paul A. 1964. “Theoretical Notes on Trade Problems.” Review of Economics and Statistics. Vol. 46, No. 2 (May): 145-154.
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